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Extremal Properties of 0/1-Polytopes of Dimension 5

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Polytopes — Combinatorics and Computation

Part of the book series: DMV Seminar ((OWS,volume 29))

Abstract

In this paper we consider polytopes whose vertex coordinates are 0 or 1, so called 0/1-polytopes. For the first time we give a complete enumeration of all 0/1-polytopes of dimension 5, which enables us to investigate various of their combinatorial éxtremal properties.

For example we show that the maximum number of facets of a five-dimensional 0/1-polytope is 40, answering an open question of Ziegler [25]. Based on the complete enumeration for dimension 5 we obtain new results for 2-neighbourly 0/1-polytopes for higher dimensions.

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Author information

Authors and Affiliations

  1. Institute for Theoretical Computer Science, Graz University of Technology, Klosterwiesgasse 32/2, Graz, A-8010, Austria

    Oswin Aichholzer

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  1. Oswin Aichholzer
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Editor information

Editors and Affiliations

  1. Institute of Mathematics and Computer Science, The Hebrew University, Givat Ram, 91904, Jerusalem, Israel

    Gil Kalai

  2. Fachbereich Mathematik MA 7-1, Technische Universität Berlin, Strasse des 17. Juni 135, D-10623, Berlin, Germany

    Günter M. Ziegler

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Aichholzer, O. (2000). Extremal Properties of 0/1-Polytopes of Dimension 5. In: Kalai, G., Ziegler, G.M. (eds) Polytopes — Combinatorics and Computation. DMV Seminar, vol 29. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8438-9_5

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  • DOI: https://doi.org/10.1007/978-3-0348-8438-9_5

  • Publisher Name: Birkhäuser, Basel

  • Print ISBN: 978-3-7643-6351-2

  • Online ISBN: 978-3-0348-8438-9

  • eBook Packages: Springer Book Archive

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